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2 years ago

A dolphin jumps 54 times in a 6 hour period. At this rate, how many jumps would be expected in a 2-hour period?

Mathematics

1 answer:

Lemur [1.5K]2 years ago

3 0

Answer:

The dolphin will jump 18 times in 2hours.

Step-by-step explanation:

Find the jumps per hour: 54/6 = 9

^This means that the dolphin jumps 9 times in an hour.

9*2 (hours) = 18

The dolphin will jump 18 times in two hours.

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What is the gradient of the blue line

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Answer:The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6. Note: Parallel lines have the same gradient.

Step-by-step explanation:

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3 years ago

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EleoNora [17]

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Step-by-step explanation:

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3 years ago

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Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer

lyudmila [28]

$f(\theta)=10\cos\theta+5\sin^2\theta$

then the derivative is

$f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta$

Critical points occur where $f'(\theta)=0$ . This happens for

$-10\sin\theta+10\sin\theta\cos\theta=0$

$-10\sin\theta(1-\cos\theta)=0$

$\implies-10\sin\theta=0\text{ or }1-\cos\theta=0$

In the first case, we find

$-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi$

In the second,

$1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi$

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3 years ago

Name each quadrilateral for which the statement is always true.

sertanlavr [38]

Answer:

rhombus

Step-by-step explanation:

Rhombus has that equiangular and is equilateral but I'm not entirely sure about this...

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3 years ago

Find values of x and y for which ABCD must be a parallelogram. The diagram is not drawn to scale.

Arturiano [62]

ANSWER
$x=4, y=8$

EXPLANATION

If ABCD is a parallelogram, then

line AB is parallel to line DC .

This means that,

$(x + 2) \degree$
and

$(2x - 2) \degree$
are alternating angles.

Alternate angles are congruent.

This implies that,

$2x - 2 = x + 2$

We group like terms to obtain,

$2x - x = 2 + 2$

This simplifies to,

$x = 4$

Also, if ABCD is a parallelogram then,

BC is parallel to AD. This means that,

$5y - 8 = y + 24$

We group like terms to get,

$5y - y = 24 + 8$

This simplifies to,

$4y = 32$

We divide both side by 4 to get,

$y = 8$

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3 years ago

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